Problem: $ \left(\dfrac{1}{81}\right)^{-\frac{3}{2}}$
Solution: $= 81^{\frac{3}{2}}$ $= \left(81^{\frac{1}{2}}\right)^{3}$ To simplify $81^{\frac{1}{2}}$ , figure out what goes in the blank: $\left(? \right)^{2}=81$ To simplify $81^{\frac{1}{2}}$ , figure out what goes in the blank: $\left({9}\right)^{2}=81$ so $ 81^{\frac{1}{2}}=9$ So $81^{\frac{3}{2}}=\left(81^{\frac{1}{2}}\right)^{3}=9^{3}$ $= 9\cdot9\cdot 9$ $= 81\cdot9$ $= 729$